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There are inertial frames of reference and the accelerated frames of reference, but are there any frames of references w.r.t. higher order derivatives of velocity? [1] [2]

For example, jerked frames of reference, snapped frames of reference, crackled frames of reference and popped frames of reference and so on?

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Of course there are, by definition. They're not exactly inertial, though. – centralcharge Sep 25 '13 at 1:50
A jerked frame of reference is an accelerated frame of reference, since in general nonzero jerk requires nonzero acceleration (except perhaps at certain instants). The only thing physically special about a frame with constant acceleration is that the fictitious forces are constant. – Ben Crowell Sep 25 '13 at 3:51
up vote 2 down vote accepted

Yes. For simplicity, consider an observer $O'$ moving in one dimension. Suppose that as measured by some other inertial observer $O$, the obsever $O'$ has the following position as a function of time \begin{align} x(t) = kt^n \end{align} where $n$ is an integer. When $n=2$ or higher, the observer has nonzero acceleration, so the a frame of reference in which he is at rest is accelerating. For $n=3$ or higher, the corresponding frame of reference will have nonzero jerk. For $n=4$ or higher...well you get the picture.

The only problem is that for $n=4$ or greater, rice crispies start appearing all over the place, and it gets really hard to make measurements.

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Rice crispies?? – Peter Mortensen Sep 25 '13 at 3:39
@PeterMortensen,_Crackle,_and_Pop#Physics – joshphysics Sep 25 '13 at 3:54

A frame of reference does not need to be inertial though, for a non-inertial frame of reference, there is, at any instant, a momentarily co-moving (inertial) reference frame or MCRF

Now suppose that a particle does accelerate. In that case, we can have an inertial frame at any event in the particle’s life by defining the momentarily comoving reference frame or MCRF for short. This is a reference frame that, at a given event, has the same velocity as the particle. If the particle is accelerating, then the MCRF will change from one event to the next, but at each point it is always an inertial frame.

Note that there is no requirement that the acceleration is uniform.

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